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Chaotic synchronization of time-delay coupled Hindmarsh–Rose neurons via nonlinear control

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Abstract

Chaotic synchronization of two time-delay coupled Hindmarsh–Rose neurons via nonlinear control is investigated in this paper. Both the intrinsic slow current delay in a single Hindmarsh–Rose neuron and the coupling delay between the two neurons are considered. When there is no control, chaotic synchronization occurs for a limited range of the coupling strength and the time-delay values. To obtain complete chaotic synchronization irrespective of the time-delay or the coupling strength, we propose two nonlinear control schemes. The first uses adaptive control for chaotic synchronization of two electrically coupled delayed Hindmarsh–Rose neuron models. The second derives the sufficient conditions to ensure a complete synchronization between master and slave models through appropriate Lyapunov–Krasovskii functionals and the linear matrix inequality technique. Numerical simulations are carried out to show the effectiveness of the proposed methods.

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Authors and Affiliations

  1. Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds Campus, Melbourne, VIC, Australia

    Imali T. Hettiarachchi, S. Lakshmanan, Asim Bhatti, C. P. Lim & Saeid Nahavandi

  2. Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam, Tamil Nadu, 638401, India

    M. Prakash

  3. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram, Tamil Nadu, 624 302, India

    P. Balasubramaniam

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  1. Imali T. Hettiarachchi
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  2. S. Lakshmanan
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Correspondence to Imali T. Hettiarachchi.

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Hettiarachchi, I.T., Lakshmanan, S., Bhatti, A. et al. Chaotic synchronization of time-delay coupled Hindmarsh–Rose neurons via nonlinear control. Nonlinear Dyn 86, 1249–1262 (2016). https://doi.org/10.1007/s11071-016-2961-4

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  • DOI: https://doi.org/10.1007/s11071-016-2961-4

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